We address propagation of paraxial Gaussian-Type beam modes in longitudinally inhomogeneous axisymmetric lens-like media, with a specific case of a transition of waveguide into antiwaveguide. Higher-order modes are described in a unified manner using a so-called secondary parabolic equation. Analyzing a linear transition from waveguide to antiwaveguide where beams are described in terms of Airy functions, we conclude that the width of a localized Gaussian-Type beam in inhomogeneous media can dramatically grow. This fact should be taken into account in numerical procedures employing summation of Gaussian beams.